Title :
On the entropy of sums
Author :
Madiman, Mokshay
Author_Institution :
Dept. of Stat., Yale Univ., New Haven, CT
Abstract :
It is shown that the entropy of a sum of independent random vectors is a submodular set function, and upper bounds on the entropy of sums are obtained as a result in both discrete and continuous settings. These inequalities complement the lower bounds provided by the entropy power inequalities of Madiman and Barron (2007). As applications, new inequalities for the determinants of sums of positive-definite matrices are presented.
Keywords :
entropy codes; random processes; entropy power inequalities; independent random vectors; positive-definite matrices; submodular set function; sum entropy; Density measurement; Entropy; History; Information theory; Linear matrix inequalities; Mutual information; Probability density function; Random variables; Statistics; Upper bound;
Conference_Titel :
Information Theory Workshop, 2008. ITW '08. IEEE
Conference_Location :
Porto
Print_ISBN :
978-1-4244-2269-2
Electronic_ISBN :
978-1-4244-2271-5
DOI :
10.1109/ITW.2008.4578674
